One of the most common investigation techniques of type-II superconductors is the transport measurement, in which an electrical current is applied to a sample and the corresponding resistance is measured as a function of temperature and magnetic field, At temperatures well below the critical temperature, T-c, the resistance of a superconductor is usually immeasurably low, But at elevated temperatures and fields, in the so-called vortex liquid phase, a substantial linear resistance is observed(1). In this dissipative state, which in anisotropic high-temperature superconductors like Bi2Sr2CaCu2O8 may occupy most of the mixed-state phase diagram, the transport current is usually assumed to flow uniformly across the sample as in a normal metal. To test this assumption, we have devised a measurement approach which allows determination of the flow pattern of the transport current across the sample. The surprising result is that, in Bi2Sr2CaCu2O8 crystals, most of the current flows at the edges of the sample rather than in the bulk, even in the highly resistive state, due to the presence of strong surface barriers, This finding has significant implications for the interpretation of existing resistivity data and may be of importance for the development of high-temperature superconducting wires and tapes.